Rahaf Mohammed al-Qunun refused to board a flight from Bangkok to Kuwait on Monday and had barricaded herself into her airport hotel room.
She said she feared her family would kill her as she had renounced Islam.
Renunciation, known as apostasy, is punishable by death in Saudi Arabia.
Ms Mohammed al-Qunun left Bangkok airport “under the care” of the UNHCR.
Thai immigration officials had said that she should return to Kuwait, where her family is.
The UNHCR said that Ms Mohammed al-Qunun’s asylum claim would take “several days” to assess.
Saudi Arabia’s embassy in Thailand has denied that its government in Riyadh requested her extradition, reports the Reuters news agency.
Arrested for disobeying your father
“My brothers and family and the Saudi embassy will be waiting for me in Kuwait,” Ms Mohammed al-Qunun earlier told Reuters.
“My life is in danger. My family threatens to kill me for the most trivial things.”
Her relatives have not commented on her claims.
Rights groups including Human Rights Watch have expressed grave concerns for Ms Mohammed al-Qunun, who had travelled to Thailand for a connecting flight to Australia, where she hoped to seek asylum.
The Australian government said it would closely monitor the case, calling Ms Mohammed al-Qunun’s allegations “deeply concerning”.
On Monday evening local time, Thailand’s chief of immigration police Surachate Hakparn confirmed that Ms Mohammed al-Qunun was “allowed to stay”, and that she “left the airport with the UNHCR”.
He earlier said the country would “take care of her as best we can”, adding: “She is now under the sovereignty of Thailand; no-one and no embassy can force her to go anywhere.
“Thailand is a land of smiles. We will not send anyone to die.”
Ms Mohammed al-Qunun tweeted that her father had arrived, “which worried and scared me a lot”, but said she felt safe “under UNHCR protection with the agreement of Thailand authorities”.
Thailand is not a signatory to the UN Refugee Convention and provides no legal protection to asylum seekers although there are more than 100,000 refugees in the country.
An injunction filed by Thai lawyers in Bangkok criminal court to stop the deportation was dismissed earlier on Monday.
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